Lexi is balancing equations. She is finding one equation to be very difficult to balance: [tex]ZnSO _4+ Li _2 CO _3 \rightarrow ZnCO _3+ Li _2 SO _4[/tex]
A. One reactant and one product needs the coefficient 2.
B. The products both need a 3 coefficient.
C. The reactants both need a 2 coefficient.
D. Atoms in the equation are already in balance.
Answer (2)
Analyze the given chemical equation and constraints.
Apply the given constraints to determine the coefficients of the reactants and products.
Check the balance of atoms for each element on both sides of the equation with the determined coefficients.
Determine that the given constraints lead to an unbalanced equation, indicating a contradiction.
Conclude that it is impossible to balance the equation with the given constraints.
Explanation
Problem Analysis Let's analyze the problem. We are given a chemical equation Z n S O 4 + L i 2 C O 3 → Z n C O 3 + L i 2 S O 4 and some constraints on the coefficients needed to balance it. The constraints are:
One reactant and one product needs the coefficient 2.
The products both need a 3 coefficient.
The reactants both need a 2 coefficient.
Atoms in the equation are already in balance.
Analyzing the Constraints Let's denote the coefficients as follows:
a Z n S O 4 + b L i 2 C O 3 → c Z n C O 3 + d L i 2 S O 4
Now, let's consider each constraint:
Constraint 1: One reactant and one product needs the coefficient 2. This means either a = 2 or b = 2 , and either c = 2 or d = 2 .
Constraint 2: The products both need a 3 coefficient. This means c = 3 and d = 3 .
Constraint 3: The reactants both need a 2 coefficient. This means a = 2 and b = 2 .
Constraint 4: Atoms in the equation are already in balance. This statement seems contradictory to the other constraints, as we will see.
Checking Atom Balance From constraints 2 and 3, we have a = 2 , b = 2 , c = 3 , and d = 3 . So the equation becomes:
2 Z n S O 4 + 2 L i 2 C O 3 → 3 Z n C O 3 + 3 L i 2 S O 4
Let's count the number of atoms of each element on both sides of the equation:
Zn: Left: 2, Right: 3
S: Left: 2, Right: 3
O: Left: 2 ( 4 ) + 2 ( 3 ) = 8 + 6 = 14 , Right: 3 ( 3 ) + 3 ( 4 ) = 9 + 12 = 21
Li: Left: 2 ( 2 ) = 4 , Right: 3 ( 2 ) = 6
C: Left: 2, Right: 3
As we can see, the number of atoms is not balanced with these coefficients.
Conclusion Since the number of atoms is not balanced with the given coefficients a = 2 , b = 2 , c = 3 , and d = 3 , the given constraints are contradictory. Therefore, it is impossible to balance the equation with the given constraints. The statement that the atoms are already in balance is false.
Final Answer The problem states that the atoms in the equation are already in balance, but the other constraints lead to an unbalanced equation. Therefore, the given conditions are contradictory, and it's impossible to satisfy all the conditions simultaneously.
Examples
Balancing chemical equations is crucial in chemistry to ensure the conservation of mass during chemical reactions. For example, in the synthesis of ammonia ( N 2 + 3 H 2 → 2 N H 3 ), balancing the equation ensures that the number of nitrogen and hydrogen atoms are the same on both sides, reflecting that atoms are neither created nor destroyed in the process. This principle is fundamental in stoichiometry, allowing chemists to accurately predict the amounts of reactants and products involved in a reaction.
The equation Z n S O 4 + L i 2 C O 3 → Z n C O 3 + L i 2 S O 4 is already balanced, making Option D the correct choice. Upon examining the counts of each atom on both sides of the equation, they match perfectly. Therefore, no additional coefficients are necessary for balancing.
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